Finite Group Databasebeta

← #20250533

Subgroups — #20250533

Order 6016.

448 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689062C211yesmaximal, characteristic, complemented
2#15689061C211yesmaximal, characteristic, complemented
3#15689061C211yesmaximal, characteristic, complemented
4#15689058C211yesmaximal, characteristic, complemented
5#15689039C211yesmaximal, characteristic
6#15689013C211yesmaximal, characteristic, complemented
7#15689011C211yesmaximal, characteristic, complemented
8#15689010C211yesmaximal, characteristic, complemented
9#15689000C211yesmaximal, characteristic
10#15688999C211yesmaximal, characteristic
11#15688994C211yesmaximal, characteristic, complemented
12#15688985C211yesmaximal, characteristic, complemented
13#15688984C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C47×#396C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×(C2×D47)⋊C4C2211yescharacteristic
26C2×(C2×D47)⋊C4C2211yescharacteristic
27C2×(C2×D47)⋊C4C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×C4×Dic47C2211yescharacteristic
31C47⋊#95C2211yescharacteristic
32C47⋊#95C2211yescharacteristic
33C47⋊#95C2211yescharacteristic
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C2×C4⋊C4×C47C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C24×C47C2311yescharacteristic
52C23×D47C2311yescharacteristic
53C22×C4×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C2×C22⋊D47—22no—
60C2×C22⋊D47—22no—
61C2×C22⋊D47—41no—
62C22×Dic47—22no—
63C22×Dic47—22no—
64C22×Dic47—41no—
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C2×C4×D47—22no—
73C2×C4×D47—41no—
74C2×C4×D47—41no—
75C4⋊C4×C47—41no—
76C4⋊C4×C47—41no—
77C4⋊C4×C47—41no—
78C22⋊C4×C47—41no—
79C22⋊C4×C47—41no—
80C22⋊C4×C47—41no—
81C22⋊Dic47—22no—
82C22⋊Dic47—41no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4—22no—
85(C2×D47)⋊C4—41no—
86(C2×D47)⋊C4—41no—
87(C2×D47)⋊C4—41no—
88C4⋊Dic47—41no—
89Dic47⋊C4—22no—
90Dic47⋊C4—41no—
91Dic47⋊C4—41no—
92C4×Dic47—41no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47#4112yes—
100C23×C47C2411yescharacteristic
101C22×D47—21no—
102C22×D47—21no—
103C22×D47—21no—
104C22×D47—21no—
105C22×D47—21no—
106C22×D47—21no—
107C22×D47#4112yes—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C22⋊D47—44no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—44no—
148C2×Dic47#4112yes—
149C4×D47—44no—
150C22×C47—22no—
151C22×C47—22no—
152C22×C47—22no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C2×#4111yescharacteristic
158C22×C47C2×#4111yescharacteristic
159C22×C47C2×#4111yescharacteristic
160C22×C47H(5,𝔽2)11yescharacteristic
161C22×C47H(5,𝔽2)11yescharacteristic
162C22×C47H(5,𝔽2)11yescharacteristic
163C22×C472−1+411yescharacteristic
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—22no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177Dic47—22no—
178Dic47—41no—
179Dic47—41no—
180Dic47—41no—
181Dic47—41no—
182Dic47—41no—
183Dic47—41no—
184#2743—471nomaximal, Sylow
185C2×C47—42no—
186C2×C47#53811yescharacteristic
187C2×C47#53911yescharacteristic
188C2×C47#54011yescharacteristic
189C2×C47#55111yescharacteristic
190C2×C47#55111yescharacteristic
191C2×C47#55211yescharacteristic
192C2×C47#56211yescharacteristic
193D47—42no—
194#400—471no—
195#400—471no—
196#400—471no—
197#399—471no—
198#396D4711yescharacteristic, complemented
199#394—471no—
200#388—471no—
201#388—471no—
202#387—471no—
203#386—471no—
204#386—471no—
205#385—471no—
206#381—471no—
207#381—471no—
208#380—471no—
209C47#274311yescharacteristic, complemented, Sylow
210C22×D4—471no—
211C23×C4—471no—
212C23×C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4C2×D4711yescharacteristic
218C2×C4⋊C4C2×D4711yescharacteristic
219C2×C4⋊C4C2×D4711yescharacteristic
220C2×C22⋊C4—471no—
221C2×C22⋊C4—471no—
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C22⋊C4—471no—
225C2×C22⋊C4—471no—
226C2×C22⋊C4—471no—
227C2×C22⋊C4C2×D4711yescharacteristic
228C2×C22⋊C4C2×D4711yescharacteristic
229C2×C22⋊C4C2×D4711yescharacteristic
230C2×C42—471no—
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95—471no—
236#95—471no—
237#95—471no—
238#95—471no—
239#95—471no—
240#95—471no—
241#95—471no—
242#95—471no—
243#95—471no—
244#95C2×D4711yescharacteristic
245C24—471no—
246C24C22×D4711yescharacteristic
247C2×D4—942no—
248C2×D4—942no—
249C2×D4—1881no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—471no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—942no—
258C22×C4—942no—
259C22×C4—942no—
260C22×C4—1881no—
261C22×C4—1881no—
262C22×C4—1881no—
263C22×C4C22×D4711yescharacteristic
264C22×C4C22×D4711yescharacteristic
265C22×C4C22×D4711yescharacteristic
266C22×C4C22×D4711yescharacteristic
267C22×C4C22×D4711yescharacteristic
268C22×C4C22×D4711yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—942no—
273C4⋊C4—1881no—
274C4⋊C4—1881no—
275C4⋊C4—1881no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—942no—
280C22⋊C4—942no—
281C22⋊C4—942no—
282C22⋊C4—1881no—
283C22⋊C4—1881no—
284C22⋊C4—1881no—
285C22⋊C4—1881no—
286C42—1881no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—472no—
294C23—941no—
295C23—941no—
296C23—941no—
297C23—941no—
298C23—941no—
299C23—941no—
300C23#1062535412yes—
301C23C23×D4711yescharacteristic
302D4—1884no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—472no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—1884no—
343C2×C4—1884no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—942no—
352C22—942no—
353C22—942no—
354C22—1881no—
355C22—1881no—
356C22—1881no—
357C22—1881no—
358C22#41×D4711yescharacteristic
359C22#41×D4711yescharacteristic
360C22C2×#1062535411yescharacteristic
361C22#1309406911yescharacteristic
362C22#1309406911yescharacteristic
363C22#1309406911yescharacteristic
364C22#1309407111yescharacteristic
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—942no—
372C4—1881no—
373C4—1881no—
374C4—1881no—
375C4—1881no—
376C4—1881no—
377C4—1881no—
378C2—42no—
379C2—1882no—
380C2#1568970511yescharacteristic
381C2#1568972211yescharacteristic
382C2#1568972311yescharacteristic
383C2#1568980011yescharacteristic
384C2#1568980011yescharacteristic
385C2#1568980911yescharacteristic
386C2#1568986811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2743
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689062C2semidirect
2. #15689061C2semidirect
3. #15689061C2semidirect
4. #15689058C2semidirect
6. #15689013C2semidirect
7. #15689011C2semidirect
8. #15689010C2semidirect
11. #15688994C2semidirect
12. #15688985C2semidirect
13. #15688984C2semidirect
14. #15688981C2semidirect
15. C47×#396C2semidirect
198. #396D47semidirect
209. C47#2743semidirect